Let f, g and h be the real valued functions defined on R as f(x)=\ ccx/(|x|), x ≠ 0 1, x=0. g(x)=\ cc(sin (x+1))/((x+1)), x ≠-1 1, x=-1. and h(x)=2[x]-f(x), where [x] is the greatest integer ≤ x. Then the value of lim x → 1 g(h(x-1)) is:

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 30 Jan, Evening shift · Q4296

JEE Main 202330 Jan, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f, g

and

h

be the real valued functions defined on

\mathbb{R}

f(x)=\left\{\begin{array}{cc}\frac{x}{|x|}, & x \neq 0 \\ 1, & x=0\end{array}\right.

g(x)=\left\{\begin{array}{cc}\frac{\sin (x+1)}{(x+1)}, & x \neq-1 \\ 1, & x=-1\end{array}\right.

and

h(x)=2[x]-f(x)

, where

[x]

is the greatest integer

\leq x

. Then the value of

\lim\limits_{x \rightarrow 1} g(h(x-1))

is :